The Walford extra, who played flower stall vendor Ina Foot on the BBC soap, was taken ill on Thursday before passing away at the weekend.
Clare made a number of appearances in the role of flame-haired Ina over the years, and a notable moment for the character came just a few months ago when her workmate Jean Slater (Gillian Wright) organised a birthday party for her at the Queen Vic.
Paying tribute to the actress, EastEnders executive producer Bryan Kirkwood commented: "Ina was a much-loved and highly valued part of the EastEnders community who will be very much missed in Albert Square. Many viewers will recognise Ina as one of the most long-standing characters on the market, where she's been helping to create the magic of Walford for 24 years."
Clare has also been praised by a number of her former colleagues on Twitter over the past 24 hours.
Writing on the social networking site, ex-cast member Robert Kazinsky (Sean Slater) described Clare as an "on-set legend" and noted that she would be "sadly missed".
Meanwhile, Sam Attwater (Leon Small) said: "R.I.P. Ina Clare, long-term supporting artist on EastEnders! Great woman to work with."
As well as her Walford role, Clare made small appearances in French and Saunders, Blake's 7 and sitcom In Sickness and in Health during her acting career.
An EastEnders spokesperson has told DS that tonight's episode of the soap will be dedicated to Clare with a screen tribute acknowledging her death.